Gap properties of harmonic maps and submanifolds
Chen, Qun ; Zhou, Zhen Rong
Archivum Mathematicum, Tome 041 (2005), p. 59-69 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

In this article, we obtain a gap property of energy densities of harmonic maps from a closed Riemannian manifold to a Grassmannian and then, use it to Gaussian maps of some submanifolds to get a gap property of the second fundamental forms.

Publié le : 2005-01-01
Classification:  53C43,  58E20 
@article{107935,
     author = {Qun Chen and Zhen Rong Zhou},
     title = {Gap properties of harmonic maps and submanifolds},
     journal = {Archivum Mathematicum},
     volume = {041},
     year = {2005},
     pages = {59-69},
     zbl = {1112.58013},
     mrnumber = {2142143},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107935}
}

Chen, Qun; Zhou, Zhen Rong. Gap properties of harmonic maps and submanifolds. Archivum Mathematicum, Tome 041 (2005) pp. 59-69. http://gdmltest.u-ga.fr/item/107935/

Chen W. H. Geometry of Grassmannian manifolds as submanifolds, (in Chinese), Acta Math. Sinica 31(1) (1998), 46–53. (1998) | MR 0951473

Chen X. P. Harmonic maps and Gaussian maps, (in Chinese), Chin. Ann. Math. 4A(4) (1983), 449–456. (1983)

Chern S. S.; Goldberg S. I. On the volume decreasing property of a class of real harmonic mappings, Amer. J. Math. 97(1) (1975), 133–147. (1975) | MR 0367860 | Zbl 0303.53049

Chern S. S.; Docarmo M.; Kobayashi S. Minimal submanifolds of a sphere with second fundamental form of constant length, Funct. Anal. Rel. Fields (1970), 59–75. (1970) | MR 0273546

Eells J.; Lemaire L. Selected topics on harmonic maps, Expository Lectures from the CBMS Regional Conf. held at Tulane Univ., Dec. 15–19, 1980. (1980)

Ruh E. A. Vilms J. The tension field of the Gauss map, Trans. Amer. Math. Soc. 149 (1970), 569–573. (1970) | MR 0259768

Sealey H. C. J. Harmonic maps of small energy, Bull. London Math. Soc. 13 (1981), 405–408. (1981) | MR 0631097 | Zbl 0444.58009

Takahashi T. Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan. 18 (1966), 380–385. (1966) | MR 0198393 | Zbl 0145.18601

Wu G. R.; Chen W. H. An inequality on matrix and its geometrical application, (in Chinese), Acta Math. Sinica 31(3) (1988), 348–355. (1988) | MR 0963085

Yano K.; Kon M. Structures on Manifolds, Series in Pure Math. 3 (1984), World Scientific. (1984) | MR 0794310 | Zbl 0557.53001